**Homework for Friday, March 17, 2000.**

You will work on this problem twice. First, you will work on it at home and you will turn in your work. This will count as one homework.

Tomorrow (Friday), you will turn in your homework at the start of class. Then, after discussing the problem for 20 minutes you will write another solution and justification.

A cab was involved in a hit-and-run accident. Two cab companies serve the city: the Green, which operates 85 percent of the cabs, and the Blue, which operates the remaining 15 percent. A witness identifies the hit-and-run cab as Blue. When the court tests the reliability of the witness under circumstances similar to those on the night of the accident, he correctly identifies the color of a cab 80 percent of the time and misidentifies it the other 20 percent.

What's the probability that the cab involved in the accident was Blue, as the witness stated?

Please do all your work on a separate sheet of paper. Write your answers in complete sentences and paragraphs.

- State your "intuitive" answer. That is, what you would think the probability is without thinking about it too hard.
- Devise a simulation of this situation that will be used
by students at another school. Since you will not be there to help them, you
must be completely explicit about how they are supposed to simulate the situation,
what they should record, and what they should calculate to estimate the probability
that the cab was red, as the witness stated.
*Write this on a separate sheet of paper.* - Draw a tree diagram. Be sure to include each step in the process that is being repeated, all the possibilities at each step, and the fraction of the time that you expect each possibility to happen.